These terms are used with respect to reasoning (epistemology) to distinguish "necessary conclusions from first premises" (i.e., what must come before sense observation) from "conclusions based on sense observation" which must follow it. Thus, the two kinds of knowledge, justification, or argument, may be glossed:

There are many points of view on these two types of knowledge, and their relationship gives rise to one of the oldest problems in modern philosophy.

The terms a priori and a posteriori are primarily used as adjectives to modify the noun "knowledge" (for example, "a priori knowledge"). However, "a priori" is sometimes used to modify other nouns, such as "truth". Philosophers also may use "apriority" and "aprioricity" as nouns to refer (approximately) to the quality of being "a priori".[3][not in citation given]

The intuitive distinction between a priori and a posteriori knowledge (or justification) is best seen via examples, as below:

A priori

Consider the proposition: "If George V reigned at least four days, then he reigned more than three days". This is something that one knows a priori, because it expresses a statement that one can derive by reason alone.

A posteriori

Compare this with the proposition expressed by the sentence: "George V reigned from 1910 to 1936". This is something that (if true) one must come to know a posteriori, because it expresses an empirical fact unknowable by reason alone.

Several philosophers reacting to Kant sought to explain a priori knowledge without appealing to, as Paul Boghossian (MD) explains, "a special faculty ... that has never been described in satisfactory terms."[4] One theory, popular among the logical positivists of the early 20th century, is what Boghossian calls the "analytic explanation of the a priori."[4] The distinction between analytic and synthetic propositions was first introduced by Kant. While Kant's original distinction was primarily drawn in terms of conceptual containment, the contemporary version of the distinction primarily involves, as the American philosopher W. V. O. Quine put it, the notions of "true by virtue of meanings and independently of fact."[5]Analytic propositions are thought to be true in virtue of their meaning alone, while a posteriori propositions are thought to be true in virtue of their meaning and certain facts about the world. According to the analytic explanation of the a priori, all a priori knowledge is analytic; so a priori knowledge need not require a special faculty of pure intuition, since it can be accounted for simply by one's ability to understand the meaning of the proposition in question. In short, proponents of this explanation claimed to have reduced a dubious metaphysical faculty of pure reason to a legitimate linguistic notion of analyticity.

However, the analytic explanation of a priori knowledge has undergone several criticisms. Most notably, Quine argued that the analytic–synthetic distinction is illegitimate. Quine states: "But for all its a priori reasonableness, a boundary between analytic and synthetic statements simply has not been drawn. That there is such a distinction to be drawn at all is an unempirical dogma of empiricists, a metaphysical article of faith."[6] While the soundness of Quine's critique is highly disputed, it had a powerful effect on the project of explaining the a priori in terms of the analytic.

The metaphysical distinction between necessary and contingent truths has also been related to a priori and a posteriori knowledge.

A proposition that is necessarily true is one whose negation is self-contradictory (thus, it is said to be true in every possible world). Considering the proposition "all bachelors are unmarried" as an example: it's negation (the proposition that some bachelors are married) is incoherent due to the concept of being unmarried (or the meaning of the word "unmarried") being tied to part of the concept of being a bachelor (or part of the definition of the word "bachelor"). To the extent that contradictions are impossible, self-contradictory propositions are necessarily false as it is impossible for them to be true. The negation of a self-contradictory proposition is thusly supposed to be necessarily true.

By contrast, a proposition that is contingently true is one whose negation is not self-contradictory (thus, it is said that it is not true in every possible world). As Jason Baehr states, it seems plausible that all necessary propositions are known a priori, because "[s]ense experience can tell us only about the actual world and hence about what is the case; it can say nothing about what must or must not be the case."[7]

Following Kant, some philosophers have considered the relationship between aprioricity, analyticity, and necessity to be extremely close. According to Jerry Fodor, "Positivism, in particular, took it for granted that a priori truths must be necessary...."[8] However, since Kant, the distinction between analytic and synthetic propositions had slightly changed. Analytic propositions were largely taken to be "true by virtue of meanings and independently of fact",[5] while synthetic propositions were not—one must conduct some sort of empirical investigation, looking to the world, to determine the truth-value of synthetic propositions.

Aprioricity, analyticity, and necessity have since been more clearly separated from each other. The American philosopher Saul Kripke (1972), for example, provided strong arguments against this position. Kripke argued that there are necessary a posteriori truths, such as the proposition that water is H2O (if it is true). According to Kripke, this statement is necessarily true (since water and H2O are the same thing, they are identical in every possible world, and truths of identity are logically necessary) and a posteriori (since it is known only through empirical investigation). Following such considerations of Kripke and others (such as Hilary Putnam), philosophers tend to distinguish the notion of aprioricity more clearly from that of necessity and analyticity.

Kripke's definitions of these terms, however, diverge in subtle ways from those of Kant. Taking these differences into account, Kripke's controversial analysis of naming as contingent and a priori would, according to Stephen Palmquist, best fit into Kant's epistemological framework by calling it "analytic a posteriori".[note 2]Aaron Sloman presented a brief defence of Kant's three distinctions (analytic/synthetic, apriori/empirical and necessary/contingent) in.[10] It did not assume "possible world semantics" for the third distinction, merely that some part of this world might have been different.

The relationship between aprioricity, necessity, and analyticity is not found to be easy to discern. However, most philosophers at least seem to agree that while the various distinctions may overlap, the notions are clearly not identical: the a priori/a posteriori distinction is epistemological, the analytic/synthetic distinction is linguistic, and the necessary/contingent distinction is metaphysical.[11]

The phrases "a priori" and "a posteriori" are Latin for "from what comes before" and "from what comes later" (or, less literally, "from first principles, before experience" and "after experience"). They appear in Latin translations of Euclid's Elements, of about 300 BC, a work widely considered during the early European modern period as the model for precise thinking.

An early philosophical use of what might be considered a notion of a priori knowledge (though not called by that name) is Plato's theory of recollection, related in the dialogue Meno (380 BC), according to which something like a priori knowledge is knowledge inherent, intrinsic in the human mind.

G. W. Leibniz introduced a distinction between a priori and a posteriori criteria for the possibility of a notion in his (1684) short treatise "Meditations on Knowledge, Truth, and Ideas".[13]A priori and a posteriori arguments for the existence of God appear in his Monadology (1714).[13]

The 18th-century German philosopher Immanuel Kant (1781) advocated a blend of rationalist and empiricist theories. Kant says, "Although all our cognition begins with experience, it does not follow that it arises [is caused by] from experience"[14] According to Kant, a priori cognition is transcendental, or based on the form of all possible experience, while a posteriori cognition is empirical, based on the content of experience. Kant states, "[...] it is quite possible that our empirical knowledge is a compound of that which we receive through impressions, and that which the faculty of cognition supplies from itself sensuous impressions [sense data] giving merely the occasion [opportunity for a cause to produce its effect]."[14] Contrary to contemporary usages of the term, Kant thinks that a priori knowledge is not entirely independent of the content of experience. And unlike the rationalists, Kant thinks that a priori cognition, in its pure form, that is without the admixture of any empirical content, is limited to the deduction of the conditions of possible experience. These a priori, or transcendental conditions, are seated in one's cognitive faculties, and are not provided by experience in general or any experience in particular (although an argument exists that a priori intuitions can be "triggered" by experience).

Kant nominated and explored the possibility of a transcendental logic with which to consider the deduction of the a priori in its pure form. Space, time and causality are considered pure a priori intuitions. Kant reasoned that the pure a priori intuitions are established via his transcendental aesthetic and transcendental logic. He claimed that the human subject would not have the kind of experience that it has were these a priori forms not in some way constitutive of him as a human subject. For instance, a person would not experience the world as an orderly, rule-governed place unless time, space and causality were determinant functions in the form of perceptual faculties, i. e., there can be no experience in general without space, time or causality as particular determinants thereon. The claim is more formally known as Kant's transcendental deduction and it is the central argument of his major work, the Critique of Pure Reason. The transcendental deduction argues that time, space and causality are ideal as much as real. In consideration of a possible logic of the a priori, this most famous of Kant's deductions has made the successful attempt in the case for the fact of subjectivity, what constitutes subjectivity and what relation it holds with objectivity and the empirical.

After Kant's death, a number of philosophers saw themselves as correcting and expanding his philosophy, leading to the various forms of German Idealism. One of these philosophers was Johann Fichte. His student (and critic), Arthur Schopenhauer, accused him of rejecting the distinction between a priori and a posteriori knowledge:

... Fichte who, because the thing-in-itself had just been discredited, at once prepared a system without any thing-in-itself. Consequently, he rejected the assumption of anything that was not through and through merely our representation, and therefore let the knowing subject be all in all or at any rate produce everything from its own resources. For this purpose, he at once did away with the essential and most meritorious part of the Kantian doctrine, the distinction between a priori and a posteriori and thus that between the phenomenon and the thing-in-itself. For he declared everything to be a priori, naturally without any evidence for such a monstrous assertion; instead of these, he gave sophisms and even crazy sham demonstrations whose absurdity was concealed under the mask of profundity and of the incomprehensibility ostensibly arising therefrom. Moreover, he appealed boldly and openly to intellectualintuition, that is, really to inspiration.

^Galen Strawson has stated that an a priori argument is one in which "you can see that it is true just lying on your couch. You don't have to get up off your couch and go outside and examine the way things are in the physical world. You don't have to do any science."[2]

^In this pair of articles, Stephen Palmquist demonstrates that the context often determines how a particular proposition should be classified. A proposition that is synthetic a posteriori in one context might be analytic a priori in another.[9]